47-i Prof. L. NatansoD on Double-Refraction 



already considered by Kundt in the Memoir referred to 

 above. In order to calculate it, Kundt had recourse to the 

 foimuise given by Stokes for the ease of steady motion, of 



which the optical experiment is a realization. Sir G. G. 

 Stokes evidently started in his analysis from the classical 

 equations o\' motion of a viscous fluid. In the particular 

 case with which we are concerned, it is seen at once that the 

 generalized equations which we have developed in our pre- 

 vious communication are incapable ot' assigning to the term 

 (1) a value other than that found by Stokes ; this results 

 from our supposition that the motion of the liquid tends to 

 become more and more steady. This conclusion is easily 

 verified. Let io=0, X=0, &>=0 in the first equation of 

 motion, § 10 of the previous communication. We then have 





_'d/ ) _ - tTJ d CV,r i d Qv.r + B C-j \ 



+-'1^'MS + S> • • • <■«> 



In this equation, the terms 



^- and e f AI__+_JL+_^) . • (3) 



approach, by supposition, the value zero. By the equations 

 given above, § 2, 



„|J! + ,|«= -£«■ ».. . . . w 



o* oy r v ' 



lastly, the last term of the second member of equation ("2 a) 

 has the value 



/a 2 o , 1 d(j </\sin 0— /*T cos © /rx 



In virtue of these results, equation (2 a) teaches us that 

 the motion of the fluid, while approaching the limiting case 

 of steady motion, must more and more accurately satisfy 

 the equations 



VM=o, m 



a^s-^- m 



which are precisely those given by Stokes. On integrating 

 and taking into account equations (1), § 1, we find from 



